The invention is based on a fuel injection pump for internal combustion engines. A fuel injection pump of this kind, known from German Offenlegungsschrift No. 26 44 698, has a first and a second relief conduit, both of which extend in the pump piston and at the pump piston circumference discharge inside the suction chamber of the fuel injection pump. The mouths of the relief conduits are disposed offset in terms of the stroke, or in other words are opened in a staggered manner by a control edge of the annular slide in the course of the pump piston stroke. Only the first relief conduit communicates directly with the pump work chamber. During an initial portion of the stroke, that is, the pre-stroke hv, of the pump piston, the second relief conduit communicates with the pump work chamber via the first pump piston valve, which is embodied by an annular groove in the pump cylinder wall and a second outlet opening of the first relief conduit. On its other end, the second relief conduit communicates with the suction chamber, in all the operating ranges except during engine starting. During starting, the outlet of the second relief conduit is closed by the annular slide, which thus forms the second valve, when it is put into the starting position. For starting the internal combustion engine driven with the fuel injection pump, the apparatus furnishes a structurally dictated constant fuel injection quantity over the course of the prestroke hv.